Metrics without Morse index bounds
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse index. Previously no such examples were known. We also discuss whether or not such bounds should hold for a generic metric and why bumpy does not seem to be the right generic notion. Finally, we mention briefly what such bounds might be used for.
Cite
@article{arxiv.math/0210290,
title = {Metrics without Morse index bounds},
author = {Tobias H. Colding and Nancy Hingston},
journal= {arXiv preprint arXiv:math/0210290},
year = {2007}
}
Comments
To appear in Duke Mathematical journal